APPLICATIONS OF DIFFERENTIAL EQUATIONS IN LIFE SCIENCES

[9] G.F. Webb, Theory of nonlinear age- dependent population dynamics Pure and applied mathematics, a program of monographs, textbooks, Lecture Notes, 1985.
[10] K.J. Engel, R. Nagel, One-parametter semigoup for Linear Evolution Equations , Springer-Verlag, New York, Berlin,[r]

w C o n v e x i t y o f t h e E u r o p e a n c o n t i n g e n t c l a i m s
In this and the following subsection we apply the comparison theorems for backward SPDEs derived in Chapter 5 to obtain some interesting conse- quences in the option[r]

1 2
( )
K p + p × q .
Depending on K = or K = , we talk about the complex or the real stability radius, respectively. Obviously, we have the estimate r ≤ r The problem of computing the stability radius for ODEs was introduced in [4-7]. Later, the r[r]

The solution to the Dynkin game is given by the following theorem, which can be obtained by a line by line analogue of Theorem 4.1 in Cvitani5 and Karatzas [2]. Here we give only the statement.
T h e o r e m 6.1. Suppose that there exists a solution (X, Y[r]

As we said in previous chapters, Integrator of Stochastic Differential Equations for Plasmas (ISDEP) is a code devoted to solve the dynamics of a minority population of particles in a co[r]

12.5.1-1. Equations solved for the highest derivative. General solution. An n th-order differential equation solved for the highest derivative has the form
y ( n )
x = f ( x , y , y x , . . . , y x ( n – 1 ) ). (12.5.1.1) The general solution of this equation depends on n a[r]

This chapter discusses the following topics. In section 2 we motivate MOC by applying it to a first-order scalar hyperbolic equation. It is useful to understand this problem because it is an essential component when studying certain classes of two-factor models in financial engi[r]

dX(t) = b(t, X(t), Y(t), Z(t))dt + a(t, X(t), Y(t), Z(t))dW(t),
(0.1) dY(t) = h(t, X(t), Y(t), Z(t))dt + Z(t)dW(t), t E [0, T],
X(O) = x, Y(T) = g(X(T)).
Here, we assume t h a t functions b, a, h and g are all deterministic, i.e., they are not explicitly d[r]

T h e o r e m 2.1. Let F = I E ~m• and ~ = m. Then (1.1) is solvable for all b, a, b, ~, x and g satisfying (1.3) if and only if (2.11) is solvable for all
c
We note t h a t by Theorem 1.2, F --- I and g = m imply Assumption A. Based on the above[r]

w U n i q u e n e s s of Adapted Solutions
In this section, we are going to establish the uniqueness of adapted weak, strong and classical solutions to our BSPDEs. From the discussion right before Proposition 1.3, we see that it suffices for u[r]

L (m) A ( f ) = [ L A ( f ( − m) )] (m) .
It turns out that the definition does not depend on the choice of integral and is therefore correct. Now, let A be a subset of d + 1 non necessarily distinct points in the convex set Ω in C n . Then it can be proven that there e[r]

3 Applications
In this section, we will present two examples in order to illustrate the validity of the above results. In the first example, we will try to prove the global existence of the solu- tions of a delay differential equation, while[r]

y(t) uniquely from its n th derivative, we need n additional pieces of information (constraints) about
y(t) . These constraints are also called auxiliary conditions. When these conditions are given at t = 0 ,
they are called initial conditions.
We discuss here two systematic procedures[r]

Every solution curve is either asymptotic to a constant solution or increases or decreases without bound.
Equilibria and Stability
Equilibrium solutions to differential equations can be classified as stable, unstable, or semistable. In Example 31.5, y = 1 and y = 3 are the[r]

Motivated by the above cited works, in this paper, a numerical
solution to (1)–(3) is computed using shifted Jacobin polynomial
basis and some operational matrices of fractional order integration and differentiation without actually discretizing the problem. The Jacobi polynomials[r]

12.7. N ONLINEAR S YSTEMS OF O RDINARY D IFFERENTIAL E QUATIONS 549
12.7.3-3. Lyapunov function. Theorems of stability and instability.
In the cases where the theorems of stability and instability by first approximation fail to resolve the issue of stability[r]

Kumasaka,1,3Gaku Ichihara,3 Masashi Kato1,3,4 1 Unit of Environmental Health Sciences, Department of Biomedical Sciences, College of Life and Health Sciences, Chubu University, Kasugai-s[r]

u + ∇ Φ ( u ) = h ( t ), where ∇ Φ denotes the gradient of the convex function Φ on R N . Copyright © 2007 C. Zhang and Y. Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in[r]

Jin Liang, James Liu, and Ti-Jun Xiao Received 18 March 2007; Accepted 26 June 2007 Recommended by Marta Garcia-Huidobro
By virtue of an operator-theoretical approach, we deal with hyperbolic singular pertur- bation problems for integrodi ff erential equations. New convergence theorem[r]